In this chapter, we focus on the nonlinear case. We show that if the relative permittivity, conductivity, or both are polynomial functions of the electric field, we can extract the sensitivities of the considered objective function or response with respect to all nonlinearity parameters using one extra simulation [4,5]. This approach is illustrated for the isotropic and nondispersive case. However, the theory can be extended to nonlinear materials with arbitrary anisotropy and dispersion profiles. The theory of adjoint sensitivity analysis of nonlinear material in computational electromagnetics is still at its initial stages. We report here on some initial results using the finite difference time domain (FDTD) method